## An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates

Please always quote using this URN: urn:nbn:de:0297-zib-62075

- In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities.

Author: | Jannes Quer, Luca Donati, Bettina Keller, Marcus Weber |
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Document Type: | ZIB-Report |

Tag: | Adaptive Importance Sampling; Girsanov; Metadynamics; Metastability; Molecular Dynamics; Non Equilibrium Sampling; Variance Reduction |

MSC-Classification: | 37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] |

60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) | |

65-XX NUMERICAL ANALYSIS | |

68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) | |

CCS-Classification: | J. Computer Applications |

Date of first Publication: | 2017/01/03 |

Series (Serial Number): | ZIB-Report (17-09) |

ISSN: | 1438-0064 |